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The phrase "a primary case" is correct and usable in written English.
It can be used when referring to a main or principal example or instance of something, often in a legal, medical, or research context.
Example: "In our study, we identified a primary case that illustrates the impact of the new policy on local communities."
Alternatives: "a main example" or "a key instance".
Exact(24)
In a day-care centre in which a primary case of meningococcal disease has occurred, the ratio has been reported at 2 to 100 per 100,000, and the danger from household contact from an infected person is believed to be 200 to 1,000 times greater than that of the general population.
Sun has used Salesforce.com as a primary case study of Sun hardware and software powering the future Saas platforms.
The serial interval can be defined as the time interval between a primary case presenting with symptoms and its infectee developing symptoms [7], [8].
Both methods assume homogenous mixing in the population, no missing data (clearly violated with the data from the Maryland communities), that a primary case experiences symptom onset prior to any cases that it infects and a completely closed system where all cases are infected by a case that has been observed.
A shorter SI was associated with antiviral administration on a primary case without statistically significant.
Serial interval is the duration between onset of a primary case and onset of its secondary cases.
Similar(36)
There is now evidence that a substantial proportion of persons exposed to a primary case-patient will have asymptomatic or very mildly symptomatic infection.
We estimated R0 by dividing the number of persons infected by a primary case-patient by the total number of primary case-patients.
A second limitation is that the calculation of the basic reproductive rate assumed that all persons infected by a primary case-patient were identified.
Fifth, if a primary case-patient was confirmed quickly, their contacts may have avoided further contact, whereas if the primary case-patient was identified later, close contact may not have been avoided.
For an ongoing epidemic, this method could be used to estimate the number of secondary cases infected by a primary case-patient, but only for periods from which all secondary cases would have been detected.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com